Given a term in a geometric sequence and the common ratio. Find the explicit formula . A) a 3 =-36 , r = 6 b) a 6 =64 , r = 2

Step-by-step explanation:

The explicit formula for a GP is expressed as

Tn = ar^{n-1}

a is the first term

n is the number of terms

r is the common ratio

a) If a3 = 36 and r = 6

a3 = ar^3-1

a3 = ar^2 = 36

ar^2 = 36

a(6)^2 = 36

36a = 36

a = 1

Get the nth term

Tn = 1(6)^{n-1}

Tn = 6^{n-1}

b)  If a6 = 64 and r = 2

a6 = ar^6-1

a6 = ar^5 = 64

ar^5 = 64

a(2)^2 = 64

4a = 64

a = 16

Get the nth term

Tn = 16(2)^{n-1}

Tn = 16*(2^n/2)

Tn = 8(2^n)

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.  

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!